%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP176-1 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 12:32:01 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    7 (   7 unt;   0 def)
%            Number of atoms       :    7 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   12 (   0 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(monotony_lub1,plain,
    ! [A,B,C] : $equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP176-1.tptp',unknown),
    [] ).

cnf(144269296,plain,
    $equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C))),
    inference(rewrite,[status(thm)],[monotony_lub1]),
    [] ).

fof(prove_p07,plain,
    ~ $equal(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),multiply(c,multiply(least_upper_bound(a,b),d))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP176-1.tptp',unknown),
    [] ).

cnf(144333056,plain,
    ~ $equal(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),multiply(c,multiply(least_upper_bound(a,b),d))),
    inference(rewrite,[status(thm)],[prove_p07]),
    [] ).

fof(monotony_lub2,plain,
    ! [A,C,B] : $equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP176-1.tptp',unknown),
    [] ).

cnf(144302296,plain,
    $equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C)),
    inference(rewrite,[status(thm)],[monotony_lub2]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[144269296,144333056,144302296,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(monotony_lub1,plain,($equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP176-1.tptp',unknown),[]).
% 
% cnf(144269296,plain,($equal(least_upper_bound(multiply(A,B),multiply(A,C)),multiply(A,least_upper_bound(B,C)))),inference(rewrite,[status(thm)],[monotony_lub1]),[]).
% 
% fof(prove_p07,plain,(~$equal(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),multiply(c,multiply(least_upper_bound(a,b),d)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP176-1.tptp',unknown),[]).
% 
% cnf(144333056,plain,(~$equal(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),multiply(c,multiply(least_upper_bound(a,b),d)))),inference(rewrite,[status(thm)],[prove_p07]),[]).
% 
% fof(monotony_lub2,plain,($equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP176-1.tptp',unknown),[]).
% 
% cnf(144302296,plain,($equal(least_upper_bound(multiply(A,C),multiply(B,C)),multiply(least_upper_bound(A,B),C))),inference(rewrite,[status(thm)],[monotony_lub2]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[144269296,144333056,144302296,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------